Was just wondering, if its 14 million to 1 to win the lotto... then what would be the odds in getting 3 numbers in exactly the same order as they are drawn aswell ?

Chris

## uk lotto odds ?

**Moderators:** Mug UK, Silver Surfer, Moderator Team

calculate A = number of permutations of the six in which any three balls appear in sequence.

Required Probability = A/B * Probability of winning the lotto.

Hope that gets you started.

suppose the drawn balls are 1,2,3,4,5,6 in that order.

The possible draw orderings with 1,2&3 in sequence:

1,2,3,x,x,x

x,1,2,3,x,x

x,x,1,2,3,x

x,x,x,1,2,3

xxx can be permuted in 6 ways: 456, 465, 645, 654, 546, 564

ie there are 6*4 = 24 ways of doing it with 1,2,3 in order.

Other sequences are: (2,3,4), (3,4,5), (4,5,6)

which gives 4 * 24 = 96 ways.

A/B = 96 / (6*5*4*3*2*1) = 2 / 15

So there is a 2/15 chance of having this outcome, on top of the odds of winning the lottery.

I hope. I now feel my reputation in fragile balance

Yes...Sarek wrote:calculate B = number of permutations of 6 balls (=6*5*4*3*2*1)

calculate A = number of permutations of the six in which any three balls appear in sequence.

Required Probability = A/B * Probability of winning the lotto.

Hope that gets you started.

suppose the drawn balls are 1,2,3,4,5,6 in that order.

The possible draw orderings with 1,2&3 in sequence:

1,2,3,x,x,x

x,1,2,3,x,x

x,x,1,2,3,x

x,x,x,1,2,3

xxx can be permuted in 6 ways: 456, 465, 645, 654, 546, 564

ie there are 6*4 = 24 ways of doing it with 1,2,3 in order.

Other sequences are: (2,3,4), (3,4,5), (4,5,6)

which gives 4 * 24 = 96 ways.

A/B = 96 / (6*5*4*3*2*1) = 2 / 15

So there is a 2/15 chance of having this outcome, on top of the odds of winning the lottery.

From a 1st glance you're correct

No I'm not Maartau!Maartau wrote: Yes...

From a 1st glance you're correct

I should know better. God I hate probability. There are overlaps in this method.

123xxx A, 234xxx B, 345xxx C, 456xxx D,

x123xx E, x234xx F, x345xx G, x456xx H

xx123x I, xx234x J, xx345x K, xx456x L

xxx123 M, xxx234 N, xxx345 O, xxx456 P

Overlaps are:

A+F 123456, 123465

A+K 123456

A+P 123456

B+G 234561, 234516

B+L 234561

C+H 345612, 345621

D+M 456123

E+J 512346, 612345

E+O 612345

F+K 123456, 623451

F+P 123456

G+L 134562, 234561

I+N 561234, 651234

J+O 162345, 612345

K+P 123456, 213456

So 15 permutations are duplicated:

a 123456 - A F K P

b 123465 - A F

c 234561 - B G L

d 234516 - B G

e 345612 - C H

f 345621 - C H

g 456123 - D M

h 512346 - E J

i 612345 - E J O

j 623451 - F K

k 134562 - G L

l 561234 - I N

m 651234 - I N

n 162345 - J O

o 213456 - K P

These 15 permutations (a-o) are seen to appear 34 times in the templates A-P, though we only need them once. Therefore 96 - 34 + 15 = 77 distinct permutations

**Required Probability = 77/720**

which is about 1 in 9

This is beginning to remind me of those unpleasant competitions they put in PC Plus magazine.

I hope you've not posted your competition slip in yet Chris.